no. 2
Strong ratio limit theorems for mixing Markov operators
Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 12 (1976) no. 2, pp. 181-191. 
@article{AIHPB_1976__12_2_181_0,
     author = {Lin, Michael},
     title = {Strong ratio limit theorems for mixing {Markov} operators},
     journal = {Annales de l'institut Henri Poincar\'e. Section B. Calcul des probabilit\'es et statistiques},
     pages = {181--191},
     publisher = {Gauthier-Villars},
     volume = {12},
     number = {2},
     year = {1976},
     mrnumber = {422577},
     zbl = {0348.60098},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1976__12_2_181_0/}
}
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Lin, Michael. Strong ratio limit theorems for mixing Markov operators. Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 12 (1976) no. 2, pp. 181-191. http://www.numdam.org/item/AIHPB_1976__12_2_181_0/

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